Respuesta :
Answer:
[tex]Var(X)=E(X^2)-[E(X)]^2 =8505-(88)^2 =761.0[/tex]
c) 761.0
Step-by-step explanation:
Previous concepts
In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".
The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).
And the standard deviation of a random variable X is just the square root of the variance.
The random variable is given by this table
X | 0 | 10 | 50 | 100 |
P(X) | 1/40 | 1/20 | 1/10 | 33/40 |
In order to calculate the expected value we can use the following formula:
[tex]E(X)=\sum_{i=1}^n X_i P(X_i)[/tex]
And if we use the values obtained we got:
[tex]E(X)=(0)*(\frac{1}{40})+(10)(\frac{1}{20})+(50)(\frac{1}{10})+(100)(\frac{33}{40})=88[/tex]
In order to find the variance, we need to find first the second moment, given by :
[tex]E(X^2)=\sum_{i=1}^n X^2_i P(X_i)[/tex]
And using the formula we got:
[tex]E(X^2)=(0)*(\frac{1}{40})+(100)(\frac{1}{20})+(2500)(\frac{1}{10})+(10000)(\frac{33}{40})=8505[/tex]
Then we can find the variance with the following formula:
[tex]Var(X)=E(X^2)-[E(X)]^2 =8505-(88)^2 =761.0[/tex]
And then the standard deviation would be given by:
[tex]Sd(X)=\sqrt{Var(X)}=\sqrt{761}=27.586[/tex]
So then the best answer for this case is:
c) 761.0
Answer:
(C) 761.0
Step-by-step explanation:
This is a grouped data with the following distance and frequency of occurrence
Formula for variance = (∑ fx²/mean)- (mean)²
x = distance
f = frequency
n = sample size
x f/n f x² fx fx²
0 1/40 1 0 0 0
10 1/20 2 100 20 200
50 1/10 4 2500 200 10000
100 33/40 33 10000 3300 330000
n ∑ fx ∑fx²
40 3520 340200
Note frequency was given as a fraction of the sample size
mean = ∑fx/n
3520/40 = 88
mean = 88
Variance = (∑fx²/mean) - (mean)²
Variance = ( 340200/40) – (88)²
Variance = 8505 – 7744
Variance = 761.0
